Structure and Properties of the Precursor/Successor Complex and Transition State of the CrCl2+/Cr2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway
The electron self-exchange reaction CrCl(OH2)5(2+) + Cr(OH2)6(2+) -> Cr(OH2)(6)(2+) + CrCl(OH2)(5)(2+), proceeding via the inner-sphere pathway, was investigated with quantum-chemical methods. Geometry and vibrational frequencies of the precursor/successor (P/S) complex, (H2O)5Cr(III)ClCr(II)(OH2)(5)(4+)/(H2O)(5)(CrClCrIII)-Cl-II(OH2)5(4+), and the transition state (TS), (H2O)(5)CrClCr(OH2)5(4+) double dagger, were computed with density functional theory (DFT) and conductor polarizable continuum model hydration. Consistent data were obtained solely with long-range-corrected functionals, whereby in this study, LC-BOP was used. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (H-ab) and the reorganizational energy (lambda) were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory. The nuclear tunneling factor (Gamma(n)), the nuclear frequency factor (nu(n)), the electronic frequency factor (nu(el)), the electron transmission coefficient (k(el)), and the first-order rate constant (ket) for the electron-transfer step (the conversion of the precursor complex into the successor complex) were calculated based on the imaginary frequency (nu double dagger) of the TS, the Gibbs activation energy (Delta G double dagger), H-ab, and lambda. The formation of the precursor complex via water substitution at Cr(OH2)(6)(2+) was also investigated with DFT and found to be very fast. Thus, the electron-transfer step is rate-determining. For the substitution reaction, only a bent TS structure could be obtained. The overall rate constant (k) was estimated as the product K-Akev, whereby KA is the equilibrium constant for the formation of the ion aggregate of the reactants Cr(OH2)(6)(2+) and CrCl(OH2)(5)(2+), Cr(H2O)(6).CrCl(OH2)(5)(4+) (IAR). k calculated for the bent and linear isomers agrees with the experimental value.